Superconducting cavities are highly susceptible to small changes in resonance frequency due to their narrow bandwidth. At the proposed linac for the TESLA Linear Collider [1] the frequency changes resulting from mechanical deformations caused by Lorentz force detuning of the pulsed cavities will be of the order of the cavity bandwidth at the design operating gradient close to 25 MV/ m. The additional power required for field control is of the order of 10 % and will be intolerably high for the planned upgrade to 35 MV/m which appears to be feasible in the near future. While passive stiffening of the cavities is already applied to the present cavity design, the further reduction of the Lorentz force detuning constant is technically challenging. Therefore we propose an active scheme which reduces the timevarying Lorentz force detuning to much less than one cavity bandwidth. If successful, the scheme will improve the power efficiency of the TESLA linac significantly
